Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.     

Efficiency analysis of Norwegian district courts

This paper examines the efficiency of the Norwegian district courts with the aim of suggesting ways of improving this efficiency. Pooling the observations for the period 1983 to 1988 efficiency measures are calculated for each court using the nonparametric data envelopment analysis (DEA) method. The results show estimates of overmanning due to technical inefficiency. Comparisons are made between the specialized city courts and the generalized rural courts. When using the yearly observations Malmquist indices are calculated to estimate the rate of productivity change. Finally the paper addresses the questions of how the information from DEA can be used by the courts to become more efficient.The editor of this paper was Knox Lovell.     

Interpretation of probability expressions by financial directors and auditors of UK companies

Probability expressions, such as ‘remote’, ‘possible’, ‘probable’ and ‘virtually certain’, have been used extensively in accounting. However, little is known about how these expressions are interpreted. It is important to understand how these expressions are interpreted by preparers of financial statements as significant inconsistencies will reduce the comparability between companies' financial statements. This paper reports the results of a survey of financial directors of large UK listed companies and UK auditors concerning the interpretation and the communication efficiency of thirty frequently used probability expressions. This paper fills two gaps in the literature. First, it surveys attitudes to probability expressions in the UK of two important groups of individuals involved in the financial reporting system and, second, it explicitly measures the ‘communication efficiency’ of these expressions. The results show that while many probability expressions were seen to have similar meaning and have a high degree of communication efficiency, several had low communication efficiency. Policy implications involve a reassessment of the use of probability expressions with low communication efficiency, and the adoption of well-understood probability expressions with high communication efficiency.     

Estimation of stochastic frontier production functions with input-oriented technical efficiency

This paper deals with estimation of input-oriented (IO) technical inefficiency using a stochastic production frontier model. Econometrically the model is similar to a class of models that arise in specifying technical inefficiency in cost-minimizing and profit-maximizing frameworks. The standard maximum likelihood (ML) method that is used to estimate output-oriented (OO) technical efficiency cannot be applied to estimate these models. We use a simulated ML approach to estimate the IO production function and compare results from the IO and OO models, mainly to emphasize the point that estimated efficiency, returns to scale, technical change, etc., differ depending on whether one uses the model with IO or OO technical inefficiency.     

Bayesian inference in limited dependent variable models. An application to measuring strike duration

This paper presents a straightforward set of Bayesian techniques for analyzing models involving limited dependent variables; the techniques are demonstrated in an analysis of Kennan's (1985) data on contract strikes in US manufacturing. The data are analyzed by deriving posterior distributions—including probability distributions—of hazard functions for strike duration using numerical Monte Carlo methods. The distributions are employed to derive coverage intervals for hazard functions, to assess the relative plausibility of nonnested hypotheses concerning the shape of the functions, and to assess the impact of industrial production on duration.     

Estimating heterogeneous capacity and capacity utilization in a multi-species fishery

We use a stochastic production frontier model to investigate the presence of heterogeneous production and its impact on fleet capacity and capacity utilization in a multi-species fishery. We propose a new fleet capacity estimate that incorporates complete information on the stochastic differences between vessel-specific technical efficiency distributions. Results indicate that ignoring heterogeneity in production technologies within a multi-species fishery as well as the complete distribution of a vessel’s technical efficiency score, may lead to erroneous fleet-wide production profiles and estimates of capacity. Our new estimate of capacity enables out-of-sample production predictions which may be useful to policy makers.     

Estimating Multiproduct Cost Functions Over Time Using a Mixture of Normals

This article proposes the use of finite mixtures of probability distributions to estimate cost functions. The mixture technique allows for the simultaneous existence and unobservability of multiple technologies of production. Technology switching by firms and conventional technical change can be studied directly. We illustrate the technique on a large sample of U.S. Savings and Loan companies, and find strong evidence of multiple technologies. We compare the mixture results to conventional stochastic cost frontier and thick frontier models, and highlight their differences.     

A process control method based on five-parameter generalized lambda distribution

The use of control charts in statistical quality control, which are statistical measures of quality limits, is based on several assumptions. For instance, the process output distribution is assumed to follow a specified probability distribution (normal for continuous measurements and binomial or Poisson for attribute data) and the process supposed to be for large production runs. These assumptions are not always fulfilled in practice. This paper focuses on the problem when the process monitored has an output which has unknown distribution, or/and when the production run is short. The five-parameter generalized lambda distributions (GLD) which are subject to estimating data distributions, as a very flexible family of statistical distributions is presented and proposed as the base of control parameters estimation. The proposed chart is of the Shewhart type and simple equations are proposed for calculating the lower and upper control limits (LCL and UCL) for unknown distribution type of data. When the underlying distribution cannot be modeled sufficiently accurately, the presented control chart comes into the picture. We develop a computationally efficient method for accurate calculations of the control limits. As the vital measure of performance of SPC methods, we compute ARL’s and compare them to show the explicit excellence of the proposed method.     

A Monte Carlo study of ranked efficiency estimates from frontier models

Parametric stochastic frontier models yield firm-level conditional distributions of inefficiency that are truncated normal. Given these distributions, how should one assess and rank firm-level efficiency? This study compares the techniques of estimating (a) the conditional mean of inefficiency and (b) probabilities that firms are most or least efficient. Monte Carlo experiments suggest that the efficiency probabilities are easier to estimate (less noisy) in terms of mean absolute percent error when inefficiency has large variation across firms. Along the way we tackle some interesting problems associated with simulating and assessing estimator performance in the stochastic frontier model.     

Information Measures in Perspective

Information-theoretic methodologies are increasingly being used in various disciplines. Frequently an information measure is adapted for a problem, yet the perspective of information as the unifying notion is overlooked. We set forth this perspective through presenting information-theoretic methodologies for a set of problems in probability and statistics. Our focal measures are Shannon entropy and Kullback–Leibler information. The background topics for these measures include notions of uncertainty and information, their axiomatic foundation, interpretations, properties, and generalizations. Topics with broad methodological applications include discrepancy between distributions, derivation of probability models, dependence between variables, and Bayesian analysis. More specific methodological topics include model selection, limiting distributions, optimal prior distribution and design of experiment, modeling duration variables, order statistics, data disclosure, and relative importance of predictors. Illustrations range from very basic to highly technical ones that draw attention to subtle points.     

Beyond profitability: effects of acquisitions on technical efficiency in the Italian pasta industry

Unlike traditional studies on the impact of ownership changes—which use either profitability measures or stock prices—this paper investigates the impact of acquisitions on acquired firms' technical efficiency. Using a panel of Italian firms in the pasta industry for the 1981–1997 period, I estimate a stochastic production frontier with exogenous factors affecting efficiency in a translog specification with non‐neutral technical progress. The main result is that acquired firms experience, within the 6 years period following the acquisition, an increase in technical efficiency of the order of 10%. This result is statistically significant and proves to be robust with respect to the inclusion of size and calendar year effects as explanatory variables of firms' inefficiency. These findings contribute to the debate on the welfare gains of ownership changes by providing evidence that mergers and acquisitions lead to cost savings, due to the reduction of acquired firms' X‐inefficiency. Copyright © 2002 John Wiley & Sons, Ltd.     

A directional slacks-based measure of technical inefficiency

Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.     

Influences of the Business Environment on Manufacturing Firms Technical Efficiencies: The Côte d’Ivoire Case

An unbalanced panel is used to estimate technical and managerial efficiency levels of manufacturing firms in Côte d’Ivoire. A stochastic frontier production model with non-neutral effects on technical efficiency of the business environment variables is specified. This specification allows to evaluate and to compare technical efficiencies and efficiency levels net of business environment influences. In order to determine net efficiency levels in the non-neutral case, a practical method based on the definition of an artificial environment is proposed. Results suggest that informal firms are less technically efficient than formal firms whereas their managerial performances are closed to those of formal firms.     

How to Construct a Random Probability Measure

This article presents an overview of several constructive methods for generating random probability measures. Applications of random probability measures include Bayesian statistics, average optimal control problems, average error bounds for numerical equation solving methods, and models for random distributions of mass in space.     

Multiple Comparisons with the Best: Bayesian Precision Measures of Efficiency Rankings

A large literature measures the allocative and technical efficiency of a set of firms using econometric techniques to estimate stochastic production frontiers or distance functions. Typically, researchers compute only the precision of individual efficiency rankings. Recently, Horrace and Schmidt (Journal of Applied Economics 15, 1–26, 2000) have applied sampling theoretic statistical techniques known as multiple comparisons with a control (MCC) and multiple comparisons with the best (MCB) to make statistical comparisons of efficiency rankings. As an alternative, this paper offers a Bayesian multiple comparison procedure that we argue is simpler to implement, gives the researcher increased flexibility over the type of comparison, and provides greater, and more intuitive, information content. For these methods and a parametric bootstrap technique, we carry out multiple comparisons of technical efficiency rankings for a set of U.S. electric generating firms, estimated using a distance function framework. We find that the Bayesian method provides substantially more precise inferences than obtained using the MCB and MCC methods.Jel Classification: C11, C32, D24.     

Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on joint chance constraints. An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.     

Random Scenario Forecasts Versus Stochastic Forecasts

Probabilistic population forecasts are useful because they describe uncertainty in a quantitatively useful way. One approach (that we call LT) uses historical data to estimate stochastic models (e.g., a time series model) of vital rates, and then makes forecasts. Another (we call it RS) began as a kind of randomized scenario: we consider its simplest variant, in which expert opinion is used to make probability distributions for terminal vital rates, and smooth trajectories are followed over time. We use analysis and examples to show several key differences between these methods: serial correlations in the forecast are much smaller in LT; the variance in LT models of vital rates (especially fertility) is much higher than in RS models that are based on official expert scenarios; trajectories in LT are much more irregular than in RS; probability intervals in LT tend to widen faster over forecast time. Newer versions of RS have been developed that reduce or eliminate some of these differences.     

Estimating the Potential Gains from Mergers

We introduce simple production economic models to estimate the potential gains from mergers. We decompose the gains into technical efficiency, size (scale) and harmony (mix) gains, and we discuss alternative ways to capture these gains. We propose to approximate the production processes using the non-parametric Data Envelopment Analysis (DEA) approach, and we use the resulting operational approach to estimate the potential gains from merging agricultural extension offices in Denmark.JEL Classification: D20, L11, L22, P41, G34     

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.     

Technical efficiency measures for dairy farms using panel data: A comparison of alternative model specifications

This article examines the impact of fixed effects production functions vis-à-vis stochastic production frontiers on technical efficiency measures. An unbalanced panel consisting of 96 Vermont dairy farmers for the 1971–1984 period was used in the analysis. The models examined incorporated both time-variant and time-invariant technical efficiency. The major source of variation in efficiency levels across models stemmed from the assumption made concerning the distribution of the one-sided term in the stochastic frontiers. In general, the fixed effects technique was found superior to the stochastic production frontier methodology. Despite the fact that the results of various statistical tests revealed the superiority of some specifications over others, the overall conclusion of the study is that the efficiency analysis was fairly consistent throughout all the models considered.